If I level up a "pure" class passive ability such as the Adept or Vanguard's Biotic Mastery and Assault Mastery, whereupon these passive state that I get a biotic (or just ambiguous) power duration/damage/cooldown enhancement, will that extend to bonus powers which are tech in nature such as if I took Energy Drain? Vice versa for Engineer and Infiltrator taking a biotic bonus power?

i think it depends on how it's stated. for example, biotic cooldown -20% will count for biotics only, but power cooldown -20% for both.